How to limit grease pencil draw area to inside of closed curve?
This can be achieved by masking a layer by another one.
On 2.91 here's how i will do it :
1 : enable masking on the desired layer

2 : select the mask layer from a list

3: turn the mask layer invisible

Step 3 can be done by several ways, like turning down layer's opacity or as Gorgious said, setting the grey material as a holdout.
Note that there is a mask toggle icon next to the layer's names in properties and dopesheet areas.